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Time evolution and ergodic properties of harmonic systems

  • I. Statistical Mechanics
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  • First Online:
Dynamical Systems, Theory and Applications

Part of the book series: Lecture Notes in Physics ((LNP,volume 38))

Abstract

We prove the existence of a time evolution and of a stationary equilibrium measure for the infinite harmonic crystal. The ergodic properties of the system are shown to be related in a simple way to the spectrum of the force matrix; when the spectrum is absolutely continuous, as in the translation invariant crystal, the flow is Bernoulli. The quantum crystal is also discussed.

Supported in part by NSF Grant GP 42225 and AFOSR Grant 73-2430B.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, Cal.

    Oscar E. Lanford III

  2. Belfer Graduate School of Science, Yeshiva University, New York

    Joel L. Lebowitz

Authors
  1. Oscar E. Lanford III
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  2. Joel L. Lebowitz
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Editor information

J. Moser

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© 1975 Springer-Verlag

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Lanford, O.E., Lebowitz, J.L. (1975). Time evolution and ergodic properties of harmonic systems. In: Moser, J. (eds) Dynamical Systems, Theory and Applications. Lecture Notes in Physics, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07171-7_3

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  • DOI: https://doi.org/10.1007/3-540-07171-7_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07171-6

  • Online ISBN: 978-3-540-37505-0

  • eBook Packages: Springer Book Archive

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